Question

2.1 Prove that for allnen, & 2+3=v* +n+3. Prov 2k + 3 = 7 n + 3. E

Use Mathematical Induction

Answer 1

- 2x+3 = n² en 3 fou dleasily À 23 - (2x) + 3 otherwise if i 24+2 = 1 4 (243) I Kai then n=2 = 12 2.5 + 3 + 2.2 +3 = 2+ 3+ 4+ 3 but n=2, n² + + 3 = 22 +243 24+2+ = 9 so son n.2, ² x+3) + 12 10+3 So our question is to prore. 2K+3 = (224) +3 – 12 + 143 that is actually we have to prove { 2K-2 na naan

that is if we proof 2 EK - nen we are done. Mone for na 4 reft hand side 2.1=2 and R.H.S 1²+ 1 = 2 so for nat this is teure. assume Mone Let us it is terme for. that пс к" So 2(1+2+. &. – – + k) = K² = K2 – 0 Mone let na Kil so 2 (1+2+ .... ak'a kar). 22 (1+2+ – – – – + k) & 2 (K41) a K2 K & 2 (K41) applying 8] 2 tas * - KCK+1) + 2 (KA1) & (Kal) (KA1+1) 2 (kit)2 + (x+1)

that is for not it is time we assume Fan nak' it is also teme and proved that fan nak't it is also tome, then by principal of induction this is teme for every near thating 22 ka n2th & NEIN & neon 2K = n2 & & Y 2K) +3= { 2K1 + 3 = EN UNEN